ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   162.   93.9 Green     
 2     2   184.   78.5 Green     
 3     3   169.   84.3 Grey      
 4     4   176.   85.5 Brown     
 5     5   172.   78.4 Blue      
 6     6   156.   75.4 Green     
 7     7   166.   74.4 Blue      
 8     8   167.   91.5 Blue      
 9     9   156.   68.2 Green     
10    10   175.   80.2 Grey      
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1]  0.4471107663  1.0469937910 -1.4730155032  1.1379430728  3.1061974959
   [6] -0.9338603890 -1.1384548289  1.0676300954  0.1096250989  2.2844647868
  [11]  0.5155317949  0.6979919050 -0.3203180785 -1.1548864026  1.2137910147
  [16] -0.8735857215 -0.0775341139 -0.8299319470 -0.7803516674  0.8709194247
  [21]  0.3290453943 -0.1722484695 -0.0749177758 -0.9367635805 -0.2479406378
  [26] -0.6975140483 -0.8948799410  0.7911009471 -1.3696173407 -0.7724715678
  [31] -1.4900744458  1.5994886904  0.1530009503  0.4003342319  1.4883796592
  [36]  0.8893018496 -1.2391940359  0.7866411381  0.7133413388  0.1603397028
  [41]  0.5658594852  2.2602871243 -0.3525294012 -1.0500753173  0.5728206827
  [46] -0.6252271488 -1.5969823230 -0.5924942876  0.5574826875  0.4899751108
  [51] -0.3500986138  1.6458957297 -0.8034012574  0.4939608705  1.1941487580
  [56] -0.0633646110 -0.5668380889  0.4713553781 -0.1955003068  0.0847828765
  [61] -0.7236370292 -0.4862382096 -1.8610738574 -0.6557178930 -1.0303048726
  [66] -0.6115010824 -0.3579028357 -1.2654312634 -0.2542965289  1.2217965866
  [71]  0.5586843967 -0.0575873669  1.3008206628 -0.1770994966 -0.9861895720
  [76] -2.7075962181 -0.2284389114  0.7179513875  0.4972390211  0.4916250355
  [81]  0.3737228893  0.1232063190 -0.4615239904 -0.7169091341 -0.6568359960
  [86]  0.1551357448  0.5047480093  0.6942995101  0.8163429688  0.2936724180
  [91]  0.8372967709  1.0041027504  0.8012833114 -1.5869305932  0.0300099866
  [96]  0.0816174827 -1.0933646033 -0.0628019505 -0.4288946197 -2.5529003552
 [101]  0.4487256170 -1.4038566314 -0.3174078351 -0.3591540735  0.2878839406
 [106] -0.5447428470 -0.5432370389 -1.1667843128  2.1253229119 -0.0250930209
 [111] -1.7433725619  0.3888965515  1.1830797077  0.2106543723  0.2004962963
 [116] -2.1074949262  0.9705528583  1.2033462706 -0.5156657958 -0.2263045018
 [121]  0.7998554182  0.2208729721 -0.7114771258 -0.2809561551  1.4245832517
 [126]  1.7601436489  0.0729279648  1.2624571066  0.3434465453 -0.7888925636
 [131]  0.8753519309 -0.0723548207 -1.2312446215 -0.2350745341  0.2460709468
 [136] -0.9776199376  0.1672057224  1.1142192991  0.0545992673  0.3782738781
 [141]  1.6649281420  2.0085887881  0.7071336134 -1.8661826166 -1.2677207603
 [146] -1.6175860298  0.5325925522 -0.3992873849  0.4696563618  0.8916104492
 [151] -0.6978417230 -0.4439371147  0.5284455518  1.9192335741 -0.9487317603
 [156] -0.8495412151 -1.1164053029 -1.1525951139  0.6292011351  1.0773291348
 [161]  1.2043635388  1.0779638169  0.1055965578 -0.4603014817 -0.0774646182
 [166]  0.7753654107  0.6746751786  1.0042184274 -0.2408733612 -0.7157004146
 [171]  1.1393560629 -0.4086428594  0.3987611712 -0.9882867235  0.8618711366
 [176] -0.2444507737  0.4716299911  0.0536323372 -0.7006223394 -0.8898219561
 [181]  0.7193423528  0.7132985858  1.4771737584  0.6543993569 -0.0863137432
 [186] -0.0362326121 -0.3925412582  1.8284981613  0.3562059377 -0.7267246089
 [191] -1.2704234642  0.2146860725 -0.3587712186 -2.0476578012  0.5269407971
 [196] -1.4279363048 -0.9451117834  2.6016579725 -0.5137515462  0.6019675127
 [201]  1.1877188124  0.3692541328  0.4430968483  1.2069126169  0.5430807482
 [206] -1.8963804269 -1.5271625589 -0.4398211867  0.8455786264 -0.7408155537
 [211] -0.5698775056 -1.2371114228  0.0125250521 -0.1669742539 -0.1347391820
 [216]  0.1712558420 -1.1343859402 -1.4340184653  2.5086014547 -0.4078995558
 [221] -2.0353565408 -0.6448114273 -0.7740495691  0.0866037849 -2.1106751604
 [226]  0.3190474877 -0.3087292423 -1.3754364579 -0.0923569247  0.3942957767
 [231] -2.2060948081  1.4866301043 -0.0227522748 -0.4710516870 -0.7255949765
 [236]  2.1471299252  0.1214303846 -1.1775209716 -1.4796605197  0.5749257442
 [241]  1.5087838857  0.8270109358  0.0596993453  1.1548879646 -1.8313758788
 [246]  0.1180733673 -0.2216496970 -1.2487481614  1.1705533540 -0.6727159606
 [251]  1.9711882598  2.7563862009  0.3813704634 -1.7606661619  1.9690184500
 [256]  0.8344628388 -1.0092971234 -0.2257133259  0.4094654921 -0.9527985670
 [261] -0.2423310234  0.4656922768 -1.2583142303  0.8897587332  1.0691701982
 [266] -1.0734843189 -0.9427756350 -0.6280278752 -0.5407506413  1.9266770877
 [271]  0.4338720259  1.0345673029 -0.3213425300 -0.5350464880  0.2431508664
 [276] -0.1575746801 -0.4528309362 -0.1529087516  0.0013775547 -0.3980698071
 [281]  2.2557711053  0.3102535267  0.2884481022  0.4900705622  0.0899513497
 [286] -0.0054538965  1.4622856033  0.4356814227  1.3312357687  0.9357219400
 [291]  0.8657692643 -1.4416820525  0.1968040276 -0.0511385524 -0.9543110712
 [296]  0.1385604550  0.2119979080  1.2637205105 -1.3513164852 -1.1920427885
 [301]  0.6091930631  0.4788913409 -0.4925525425  0.2248690097  1.4135817605
 [306] -0.8764913969  1.2072038792 -0.9287763506 -0.0745673297 -0.0247398420
 [311] -0.2833749833 -0.3677141430 -0.5052213371  2.9856138875  0.9409404774
 [316] -0.7713015619 -1.9182655505  1.6278358208 -0.8537572468  0.4621888493
 [321] -0.1186347082  0.0586707666  1.9700787678  0.9771766993  0.3448156212
 [326]  0.2478591146 -0.6085797540  0.0226721384 -0.6324675126  0.6422790323
 [331] -0.9002571089 -0.4525140587 -0.6221562867 -1.9965265691 -0.7400410163
 [336] -2.2886867097 -0.6183457535 -1.6696289173  0.2469569472  0.9984418067
 [341]  0.0160074296  1.2794163172  1.8584097615 -0.8260579596 -0.1083375630
 [346]  0.0472133989 -0.3406577460  0.7395720489  1.9137977792 -1.5034556607
 [351]  0.9717270400  0.0809008202  0.7465862865  0.0426597628  2.8351790953
 [356]  0.5191841325 -1.8956645810  0.1186462833 -1.0678935376  1.7241580555
 [361]  0.6578555134 -0.3783788141  0.3399590344 -0.0579080166 -0.5243264644
 [366] -0.0933376897  0.1283356467 -0.5092837403  0.4073436493 -0.9889982663
 [371]  1.3231850433  0.8493446714 -0.3907809341 -0.5227916397  0.6873491314
 [376]  0.4549774154 -0.7140808053  0.5965833979 -0.4115162362 -0.1871297322
 [381]  0.4667966247 -0.5855088918 -0.9583485559 -1.1800031340 -0.0566878867
 [386] -0.1248460303  0.4235117077  0.2936620574  1.6986731157  0.8893823323
 [391] -0.2807927701 -1.1050437872  0.4393111997  1.4096179442 -0.7501935887
 [396] -0.2954135367  1.3187783378 -0.9662185456 -1.4198339182  0.6032269062
 [401] -0.6122848803 -0.4303584682  1.7431642925 -1.5016685299 -1.9960374698
 [406] -1.6086119998  0.9461926291 -0.3292224450 -1.8077282592  1.2445733139
 [411] -1.5699567560 -0.6992000311 -0.5427487831  0.3705289899 -0.2103936443
 [416] -0.4400036720 -1.3578670064 -0.1884540110 -2.1075149368 -0.6821750535
 [421]  0.0801957038  0.8605782988  0.4389486356  1.4303389117 -0.7596770513
 [426]  0.3789813907  0.3922770486 -1.0616293329 -1.2939607217  0.8943846694
 [431]  0.6562941794  2.1677963388 -0.4367183917 -0.0344721568  0.0154982399
 [436]  1.0578818546 -0.1871505324 -0.2774286993 -1.5455726055 -0.5648276112
 [441] -2.4594100746 -1.8611076335  0.5940602990  0.1513850785  0.1052156278
 [446]  0.7384537643  2.1061733510 -0.0403014242 -0.3990844944 -0.1640367291
 [451]  0.6502388600  1.4532859481 -1.5584116195 -0.0996831468 -0.3869175696
 [456]  0.1786930891 -0.8842433568 -0.5711322846  0.6676714256 -0.9054648311
 [461]  0.3183614584  0.9744252568  1.9023997409  0.8131611946  1.5288130619
 [466] -0.1682511019  1.7343779106  1.0267487215 -0.5842595368 -0.0326914017
 [471] -0.5043571340  1.1268082812 -1.2484235009 -1.9219796668 -0.9722574614
 [476] -0.2547257543 -0.5020513894  1.3388575838 -0.4432502191  1.4651608185
 [481]  0.0968019965  1.9669929264 -1.1368364092  0.6051958569  1.7030827116
 [486]  0.6708910899 -0.9309394141 -0.9335291631 -0.9920110979  0.7887104056
 [491] -0.0830522744 -0.3348860045  0.3958321374  0.9023506483 -1.0273258405
 [496]  0.9783016332 -0.0903436641  0.2011618668 -1.1465700392 -1.6314466886
 [501] -1.7905108634  1.0003987418  1.3488458068  0.0653686850 -0.8579017617
 [506]  2.5204835439  2.1569074628  0.1622402438 -1.4282326183 -3.3666012319
 [511]  1.4743945016  1.2941137621  0.5737664930  0.3371734931 -0.2508666223
 [516] -0.1000335568  1.6698890673  1.1123442269  0.4741496751  0.0775556916
 [521]  0.1798076838 -0.5570931700 -1.4952830576  0.0258809529  0.1022874493
 [526] -0.0947980715  1.7263620079  0.2932019743  1.0278628515  0.3248032393
 [531]  0.2093913071 -0.3741261521 -0.3960154046  0.4868705801  1.0332282132
 [536] -1.2307470817  1.1738575118 -0.5859108973  1.3140991768 -0.0340668660
 [541] -1.9507092066 -2.1236986355 -0.2391265383 -0.7026677133  0.5319713963
 [546]  0.1039035445  0.4740384863 -1.2471356443  1.8059736323  1.0889780354
 [551] -0.4501110523 -0.4528829497  1.6759860365 -1.8157830907 -1.2313012422
 [556] -0.4456304722  0.5415929513  0.5828372270  0.8043220208  1.6140542052
 [561]  1.4267912910 -0.6995188315 -0.3714086631 -0.1926886638 -0.2353315330
 [566]  0.8955545098 -0.2969119348 -0.9176412966 -2.1248209177 -0.7589930378
 [571] -0.7479722725 -0.4581580224  0.7060459263  0.4103480280 -0.4783415217
 [576]  0.9695219461 -1.5776948247  0.1658045798 -0.0451788721  0.7913182543
 [581]  0.7562138198 -1.7322301709 -0.2988019726  0.8204618910 -1.3421384767
 [586] -0.7249249538 -1.2705149621  1.4587366026  0.6023825296  0.5821387216
 [591]  0.7871912612 -0.5844039312  0.4859556283  0.6738366603 -0.1762692861
 [596] -0.2873593585  0.2884457583  1.0111395803  1.4734367251  0.2776729122
 [601]  0.4067240157 -0.5631215267  0.1826839530  0.4210467188  2.1174753129
 [606]  0.1726453779 -0.3862165720 -0.9209732676 -0.0595766414  0.0979806166
 [611] -0.0481771456 -1.4265951955  0.0756834850 -0.0942776887 -1.0492016375
 [616]  1.5766558992  2.6556838044 -0.9095650066 -0.2243306459  1.5829769415
 [621]  0.3711401213 -1.4419041586  0.3905483650  1.3716045256 -0.7552048472
 [626] -0.1147962977  0.8460512639  1.0979861973  1.4868069118  0.4356316149
 [631]  0.7780343101 -0.6917643170  0.0649237659  0.0127671799  0.2510090877
 [636]  0.4076425940  0.8976147610 -0.4342623104 -0.1936570089 -0.5002195706
 [641] -0.2784511235  0.6269477017 -0.9795328082  1.4582661406 -1.7100922688
 [646] -0.3356018674  0.2647241604  0.4181298543  1.6487724342  1.4802296767
 [651] -0.0855657535 -0.3336942369  0.2718665701  0.8460714225  0.7400126743
 [656] -0.5063133653  0.6226200846 -1.3499146316 -0.9220270524 -0.1052324549
 [661] -1.3568512834  1.0520750710 -0.5013666060 -0.2879874482  0.4862668710
 [666] -0.0682754076 -0.6863343030 -0.5428569549  0.6699604872 -0.5192338866
 [671] -0.0202733386 -1.3985573738  0.2391801576  0.6093054155  1.2333687445
 [676]  0.6952659835  1.3644908845  0.0467399519  0.7893346961  0.8602016036
 [681]  1.2979249086 -0.7497434767  0.4639878440  0.3956281667  0.6631540852
 [686]  1.1817723454 -0.0726676322 -0.4374133470 -0.6166056886  1.4797117067
 [691]  0.4800182051  1.6418127575 -1.0161208792  0.0337854074  0.7361156842
 [696] -0.9421056618  0.0163960295  0.0586314093 -1.1893255167 -0.7530188607
 [701] -0.4197603707 -0.4565803168  0.6501915152 -0.0163495615 -0.8378256045
 [706] -0.3616651217 -0.0071495705 -0.1027545973 -0.6965698451 -1.5062822373
 [711]  0.7313533107  0.5026411819 -0.4260872284  0.6430407080 -1.4239950340
 [716]  0.3653757126 -0.6119277870  1.7075149292  0.8310006455  0.5471882519
 [721]  0.3324079715  0.0623010200 -1.1329052892 -1.1904956881  3.0499883572
 [726] -0.9769025189 -1.1981282062  0.6614753655  1.3154431820  1.5186813703
 [731] -0.9222478051 -1.2747362345 -0.7815085990  0.3300628631 -0.9570078842
 [736] -0.3213958169  0.0858607675 -0.6688448508  1.1180014062  1.0787495060
 [741] -0.2193165609  0.2418022360 -0.4465359210  1.3636048540 -1.9672479233
 [746] -0.3975668007  0.1264209143  1.4256528722 -1.0021727591  1.7072985552
 [751]  0.9010232073 -1.8807587016  0.4353262050 -0.4726495132 -0.9631740228
 [756] -0.1874481046 -1.5395734824  1.6844155272  0.8489698567  0.4274346067
 [761]  0.0273142342 -0.3084820557 -0.1928580433 -0.5978780889 -0.4102577341
 [766] -0.6188171381  1.2559732628  0.9079795708 -0.2054352771 -1.7659582893
 [771]  0.1283852683 -0.0930200918 -0.3777588821  0.7808100925  0.0781580235
 [776]  1.0232721913  0.2720779497  1.3145854803  1.4556138952 -1.1734804128
 [781] -0.6521693643  0.5046706774  1.4812892371 -0.0208526309 -0.6364031089
 [786] -0.0344192291 -0.4524948610 -0.3755242515  0.8477240980  1.4560985424
 [791]  0.8027386188  0.8708441904 -0.9584624848  0.3844913888  1.4321643966
 [796] -0.5456994827  0.7987175567 -0.4427381393  0.9729920113 -1.2581840930
 [801]  0.1069556426 -0.8848747462 -1.2466429051 -1.5998982762  0.6188494647
 [806]  0.4086813848 -0.0006716325  0.3771743898  1.3257775310  1.0728856607
 [811]  0.4884366941 -0.8966544330 -0.0024070346  0.2085343600 -0.2685436827
 [816] -1.3233238648 -0.3361695158  0.5829686272 -0.3854552352  0.0477093512
 [821]  0.0128901374  0.8682574693 -0.7713236063 -0.9452390500  0.5203831323
 [826] -1.4247890963 -1.2562170464 -0.4195398160 -0.1269317526 -2.6564805919
 [831]  1.2081918759  0.6328578560 -0.3980179913  1.0803485098  3.0910645782
 [836]  0.1867531373  0.4318802076  0.0116372003 -1.2595769422  0.0493905363
 [841]  1.2227989460  0.2616495332 -0.6617558030  2.2583968638 -0.0465578681
 [846] -0.5567821842  0.1515812764  0.6332796649  0.0579813371  0.2664422717
 [851]  1.6345758325 -0.5940417326 -0.8410186881  0.9820483389 -0.2433722574
 [856]  1.2858316635 -0.3332799656 -0.3848890127  0.4344490028  0.3446435419
 [861]  1.4873221027  0.3213998907  1.2518582543  0.8879813086  0.5294475617
 [866] -0.8983311038 -0.0907316942  2.1253004396  1.4074244832  0.3799114893
 [871]  1.6861420794 -0.5766936196 -0.6932077526 -0.4537679636  0.7367995119
 [876]  0.0945989697 -0.0126705625  2.4965358968 -0.3509072524  1.1869196228
 [881]  0.4008435476  1.3630568767 -0.5946453679 -0.6645272708  0.0214734371
 [886]  1.1854532299 -0.6729374772  1.2567958126 -1.3068698014  0.5821068983
 [891] -0.1641924621 -0.2638567260 -0.8159688420  0.6298299921 -1.1179454092
 [896] -0.5603888968 -1.1347506435 -0.2155125316  1.1821577972 -0.1522819425
 [901] -2.3232903643 -0.3205479772  0.2133635054  0.7639668665  0.7753558337
 [906] -0.4216407930 -0.3151138922 -0.4799208637  0.8562552299  1.3240908198
 [911] -0.0464474854 -0.3529868775  0.3066143627 -0.6180988481  1.0778577181
 [916]  0.3484140189  1.4259975497  0.4682817740  0.9213570512  0.4378744024
 [921]  0.3516368676 -0.6168271561 -1.5086053375 -0.7848424650 -1.5843988191
 [926] -1.2023789409 -0.4538670238  0.5084514331  1.6249655279  0.3503053058
 [931] -0.7786027472 -0.2645179973  0.7629739233  1.7860156099  0.7012796662
 [936] -1.8106668449 -0.0875308393  2.2199367998 -1.4490046449 -0.0237106937
 [941] -1.3710846032 -0.9366312898 -0.1968744522  0.7309535063 -1.3292111217
 [946] -0.5636820838 -1.0069759893 -1.3106424693 -1.1791165150 -0.6287384778
 [951] -0.0231156623  0.4817533621 -1.8932858446  2.1054639707 -0.0265090348
 [956] -1.3621719886 -1.4120079067 -0.4727487198  1.4573477914  0.6011654229
 [961]  0.0811049706  0.4830118169 -0.8420608378  0.4133075315 -1.5797856289
 [966] -0.1688644023 -1.3862375723  1.5295382796  0.4433089098  0.6099746945
 [971]  0.1757184490  0.5132320486 -1.3529416645  0.3635860371  0.3176225588
 [976] -0.8333241708 -0.6184798946  0.1522649132 -0.3887699307  0.8149133106
 [981] -0.0476553191  1.2610721985  0.7367703533 -0.4806652169  1.1113507968
 [986] -0.2525830409 -0.9540692892  0.4943383098  1.4609753764  0.6490836369
 [991] -1.4917499616  1.2756649789  0.2671202655  0.2234552944  2.7348918542
 [996] -0.0973168444 -0.1294142627  0.5783448169 -0.3597531047 -0.6849058460

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0
  [38] 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1
  [75] 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1
 [112] 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0
 [149] 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1
 [186] 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0
 [223] 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0
 [260] 0 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0
 [297] 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0
 [334] 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1
 [371] 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0
 [408] 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1
 [445] 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 1
 [482] 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1
 [519] 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0
 [556] 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 1 0 1
 [593] 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0
 [630] 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0
 [667] 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0
 [704] 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1
 [741] 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1
 [778] 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1
 [815] 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1
 [852] 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1
 [889] 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1
 [926] 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0
 [963] 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0
[1000] 0

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   162.   93.9 Green      A    
 2     2   184.   78.5 Green      A    
 3     3   169.   84.3 Grey       A    
 4     4   176.   85.5 Brown      B    
 5     5   172.   78.4 Blue       B    
 6     6   156.   75.4 Green      B    
 7     7   166.   74.4 Blue       B    
 8     8   167.   91.5 Blue       B    
 9     9   156.   68.2 Green      B    
10    10   175.   80.2 Grey       A    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups